Method and apparatus for blind detection of interference parameters in LTE system

ABSTRACT

A method and an apparatus. The method includes receiving a signal including a serving signal and an interference signal; applying a Gaussian approximation (GA) on the serving signal and the interference signal; determining likelihood metrics for hypotheses on a rank of the interference signal, a precoding matrix index, and power on the GA-applied interference signal based on a covariance matrix for each of the hypotheses; and selecting one of the hypotheses that maximizes one of the likelihood metrics.

PRIORITY

This application is a continuation application of U.S. patentapplication Ser. No. 15/144,398, filed on May 2, 2016 in the UnitedStates Patent and Trademark Office, which claimed priority under 35U.S.C. § 119(e) to a U.S. Provisional Patent Application filed on Feb.18, 2016 in the U.S. Patent and Trademark Office and assigned Ser. No.62/296,804, the entire contents of each of which are incorporated hereinby reference.

FIELD

The present disclosure relates generally to telecommunications, and moreparticularly, to a method and an apparatus for blind detection ofinterference patterns in a long term evolution (LTE) system.

BACKGROUND

Network assisted interference cancellation and suppression (NAICS) hasattracted a lot of attention in the 3^(rd) Generation PartnershipProject (3GPP) due to its capability to increase transmission rate andis adopted as an optional feature in Release 12 of the 3GPP. In thepresence of an interference signal, joint maximum-likelihood (ML)detection can provide a significant performance gain. However, toperform joint detection, interference dynamic parameters such aschannel, transmission mode (TM), number of cell-specific referencesignal (CRS) ports (TM1-TM7), number of demodulation reference signal(DMRS) ports (TM8-TM10), precoding power (P_(A)) and transmitted power(P_(B)) (TM1-TM7), rank indicator (RI), pre-coding matrix indicator(PMI), and modulation order must be known.

A conventional receiver considers co-channel interference as additivewhite Gaussian noise (AWGN). The NAICS was introduced to address thecapacity and performance issues in LTE downlink channels, including thehigh complexity of conventional joint ML estimation of traffic to pilotratio (TPR), rank, precoding, and modulation order. Due to the limitedback-haul and control channel resources from an evolved node B (eNB) toa user equipment (UE), it is not be possible to provide a UE withinformation regarding all the interfering cell dynamic parameters. Aportion of the dynamic parameters may be provided as side information tothe UE so that other parameters are left for blind-detection by the UE.

SUMMARY

According to one embodiment, a method includes receiving a signalincluding a serving signal and an interference signal; applying aGaussian approximation (GA) on the serving signal and the interferencesignal; determining likelihood metrics for hypotheses on a rank of theinterference signal, a precoding matrix index, and power on theGA-applied interference signal based on a covariance matrix for each ofthe hypotheses; and selecting one of the hypotheses that maximizes oneof the likelihood metrics.

According to one embodiment, an apparatus includes an antenna forreceiving a signal including a serving signal and an interferencesignal; and a processor configured to apply a GA on the serving signaland the interference signal, determine likelihood metrics for hypotheseson a rank of the interference signal, a precoding matrix index, andpower on the GA-applied interference signal based on a covariance matrixfor each hypotheses; and select one of the hypotheses that maximizes oneof the likelihood metrics.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects, features, and advantages of certainembodiments of the present disclosure will be more apparent from thefollowing detailed description, taken in conjunction with theaccompanying drawings, in which:

FIG. 1 is a block diagram of an apparatus, according to an embodiment ofthe present disclosure; and

FIG. 2 is a flowchart of a method, according to an embodiment of thepresent disclosure.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE PRESENT DISCLOSURE

Hereinafter, embodiments of the present disclosure are described indetail with reference to the accompanying drawings. It should be notedthat the same elements will be designated by the same reference numeralsalthough they are shown in different drawings. In the followingdescription, specific details such as detailed configurations andcomponents are merely provided to assist the overall understanding ofthe embodiments of the present disclosure. Therefore, it should beapparent to those skilled in the art that various changes andmodifications of the embodiments described herein may be made withoutdeparting from the scope and spirit of the present disclosure. Inaddition, descriptions of well-known functions and constructions areomitted for clarity and conciseness. The terms described below are termsdefined in consideration of the functions in the present disclosure, andmay be different according to users, intentions of the users, orcustoms. Therefore, the definitions of the terms should be determinedbased on the contents throughout the specification.

The present disclosure may have various modifications and variousembodiments, among which embodiments are described below in detail withreference to the accompanying drawings. However, it should be understoodthat the present disclosure is not limited to the embodiments, butincludes all modifications, equivalents, and alternatives within thespirit and the scope of the present disclosure.

Although the terms including an ordinal number such as first, second,etc. may be used for describing various elements, the structuralelements are not restricted by the terms. The terms are only used todistinguish one element from another element. For example, withoutdeparting from the scope of the present disclosure, a first structuralelement may be referred to as a second structural element. Similarly,the second structural element may also be referred to as the firststructural element. As used herein, the term “and/or” includes any andall combinations of one or more associated items.

The terms used herein are merely used to describe various embodiments ofthe present disclosure but are not intended to limit the presentdisclosure. Singular forms are intended to include plural forms unlessthe context clearly indicates otherwise. In the present disclosure, itshould be understood that the terms “include” or “have” indicateexistence of a feature, a number, a step, an operation, a structuralelement, parts, or a combination thereof, and do not exclude theexistence or probability of addition of one or more other features,numerals, steps, operations, structural elements, parts, or combinationsthereof.

Unless defined differently, all terms used herein have the same meaningsas those understood by a person skilled in the art to which the presentdisclosure belongs. Such terms as those defined in a generally useddictionary are to be interpreted to have the same meanings as thecontextual meanings in the relevant field of art, and are not to beinterpreted to have ideal or excessively formal meanings unless clearlydefined in the present disclosure.

According to an embodiment of the present disclosure, blind interferenceparameter identification is provided which may be used in NAICS LTEscenarios to improve overall serving cell detection quality with jointdetection of serving and interference signals. The present disclosuremay be applied to CRS-based TMs, i.e., TM1-TM7 with two CRS antennaports. In addition, the present disclosure may be applied to one CRSantenna port. The number of CRS antenna ports may be provided to a NAICSUE by radio resource control (RRC) signaling.

According to an embodiment of the present disclosure, a low complexityidentification scheme for rank, precoding and transmitted power (P_(A)for non-CRS OFDM symbols and P_(B) for CRS OFDM symbols) identificationis provided. The embodiment may be part of a modem to support NAICS asone of the LTE Release 12 features and support interference parameteridentification. The present disclosure may provide identification ofTPR, precoding index, and rank of the interference signal. TPRrepresents the power ratio of data symbols to pilot symbols. The presentdisclosure applies GA over both serving and interfering signals tosimplify the identification of TPR and precoding methodology. Thepresent disclosure may also be implemented after serving signalcancellation which is a special case of interference identification inthe presence of both serving and interfering signals. GA of theinterference and serving signals allows the present disclosure to detectTPR, distinguish between rank 1 and rank 2/space frequency blockdecoding (SFBC), detect rank 1 precoding, and provide rank 2 precodingidentification to differentiate rank 2 and SFBC cases.

According to an embodiment of the present disclosure, ML identificationwith Gaussian approximation scheme (ML-GA) may be further approximated.This reduces the number of required divisions and logarithm calculationsby a factor of K, where K is the number of resource elements (REs) usedin detection. For example, only one division and one logarithmcalculation may be required per resource block (RB).

In an embodiment of the present disclosure, GA reduces interferenceparameter complexity. In addition, joint detection of TPR, rank andprecoding after GA is provided in a low complexity scheme. Furthermore,low complexity rank 2 precoding identification after rank 2 interferenceis determined is provided.

FIG. 1 is a flowchart of a method of blind detection of interferenceparameters, according to an embodiment of the present disclosure. In thepresence of several interfering cells, an NAICS UE may determine thestrongest interfering cell among RRC-signaled candidate cells based onreceived power observations such as received signal power (RSP). Thatis, the present disclosure may process a dominant interference signal.

Referring to FIG. 1, a signal is received at 101, where the signal mayinclude a serving signal and an interference signal. According to anembodiment of the present disclosure, CRS based transmissions, i.e.,TM1-TM7, may be processed. The number of CRS antenna ports may beprovided to an NAICS UE by RRC signaling. In the case of one CRS antennaport, TPR and modulation order may be identified and in the case of twoCRS antenna ports, TPR, rank, precoding and modulation order may beidentified. Rank, precoding, and TPR identification for two CRS antennaports may be provided. In addition, TPR identification for one CRSantenna port may be provided.

Considering only a dominant interfering UE, a received signal in thepresence of a serving signal on a kth RE may be described as in Equation(1) as follows:y _(k) =H _(k) ^(S) x _(k) ^(S)+ρ_(I) H _(k) ^(I) x _(k) ^(I) +n_(k)  (1)where H_(k) ^(m) represents an effective channel matrix from a servingeNodeB to a UE for m=S and from an interfering cell to the UE for m=I,where ρ_(I) represents a TPR of the interfering signal, x_(k)^(m)=[x_(k) ^(m,1), . . . ,x_(k) ^(m,l) ^(m) ]^(T) transmit signalvector, l_(m) indicates a number of transmission layers, and n_(k) is anAWGN vector with covariance E{n_(k)n_(k) ^(H)}=σ²I. The i-th layer'stransmit symbol x_(k) ^(m,i) is chosen from some constellation

_(i) ^(m) with cardinality of |

_(i) ^(m)|, where |

_(i) ^(S)| is known, |

_(i) ^(l)|=2^(q) is unknown, and an NAICS UE blindly detects q. Asdescribed above, H_(k) ^(m) represents an effective channel matrix whichmay be written in terms of matrix G_(k) ^(m) and precoding matrix P^(S)as H_(k) ^(S)=G_(k) ^(S)P^(S) and H_(k) ^(I)=G_(k) ^(I)P^(I,l) ^(I,p) .

An NAICS UE may estimate G_(k) ^(S), but P^(I,l) ^(I,p) is unknown, withp denoting an interference precoding index and l_(I) denoting aninterference rank. For rank 1, the precoding matrices are

${P^{I,1,0} = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\1\end{bmatrix}}},{P^{I,1,1} = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- 1}\end{bmatrix}}},{P^{I,1,2} = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\j\end{bmatrix}}},{P^{I,1,3} = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- j}\end{bmatrix}}},$and for rank 2 the precoding matrices are

${P^{I,2,0} = {\frac{1}{2}\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}}},{P^{I,2,1} = {{\frac{1}{2}\begin{bmatrix}1 & 1 \\j & {- j}\end{bmatrix}}.}}$

According to an embodiment of the present disclosure, an NAICS UE mayblindly detect an interference rank l_(I), an interference precodingindex p, and an interference TPR 92 _(I).

At 103, the present system determines whether the serving signal in thereceived signal is cancelled or not.

In NAICS, if a cyclic redundancy check (CRC) of a serving signal fails,then interference parameter identification is performed to enable jointdetection and improve serving signal detection performance. The decoderoutput is employed after serving signal decoding in interferenceparameter identification by soft inference cancellation. If {circumflexover (x)}_(k) ^(S) is defined as the soft estimation of the servingsignal, after cancellation, Equation (2) is obtained as follows:ŷ _(k) =y _(k) −H _(k) ^(S) {circumflex over (x)} _(k) ^(S)=ρ_(I) H _(k)^(I) x _(k) ^(i) +H _(k) ^(S)(x _(k) ^(S) −{circumflex over (x)} _(k)^(S))+n _(k)  (2)

If a serving signal is cancelled from the received signal then a sampledcovariance matrix of serving-signal-cancelled received signal isdetermined at 105.

If a serving signal is not cancelled from the received signal then asampled covariance matrix of the received signal is determined at 107.

Furthermore, ŷ_(k) may be modified to be more like white noise (e.g.,whitened), where, for a covariance matrix of noise and residual signal,Equation (3) as follows:{circumflex over (R)} _(k) =L _(k) L _(k) ^(H)=σ² I+H _(k) ^(S) E{(x_(k) ^(S) ˜{circumflex over (x)} _(k) ^(S))(x _(k) ^(S) ˜{circumflexover (x)} _(k) ^(S))^(H)}(H _(k) ^(S))^(H)   (3)and E{(x_(k) ^(S)−{circumflex over (x)}_(k) ^(S))(x_(k) ^(S)−{circumflexover (x)}_(k) ^(S))^(H)} may be calculated using decoder outputlog-likelihood ratios (LLRs). Therefore, by applying whitening matrixW_(k)=L_(K) ⁻¹, Equation (4) is obtained as follows:y′ _(k) =W _(k) ŷ _(k)=ρ_(l) W _(k) H _(k) ^(I) x _(k) ^(I) +n′_(k)  (4)

The system model with serving signal cancellation as applied in Equation(4) above may be considered as a variation of Equation (1) above withH_(k) ^(S)=0.

Following the model provided in Equation (1) above, with known G_(k)^(S), P^(S) and

_(i) ^(S) for i ∈(1, . . . , l_(S)), Equation (5) is defined as follows:

ρ I , p , l I , q = ∏ k = 1 K ⁢ 1  χ S  ⁢ ∑ x k S ∈ χ S ⁢ 1  χ l I , q I ⁢ ∑ x k I ∈ χ l I , q I ⁢ e -  y k - G k S ⁢ P S ⁢ x k S - ρ I ⁢ G k S ⁢ I, l I , p x k I  σ 2 ( 5 )

A joint ML detection for l_(I), p, ρ_(I) and q may be obtained inEquation (6) as follows:({circumflex over (ρ)} _(I) ,{circumflex over (p)},{circumflex over (l)}_(I) ,{circumflex over (q)})=argmax _(ρ) _(I) _(,p,) _(l) _(I,q)

_(ρ) _(I) _(,p,) _(l) _(I,q)  (6)

After either 105 or 107, likelihood metrics for hypotheses oninterference signal rank, precoding matrix index (PMI), and power withGA on the interference signal are determined at 109.

According to an embodiment of the present disclosure, sequentialdetection of different parameters is provided. Joint identification ofTPR and covariance matrix index (cmi) may be a first step of thesequential detection.

According to an embodiment of the present disclosure, the present systemand method applies GA over both interfering and serving signals as inEquation (7) as follows:x _(k) ^(m) ˜N(0,I _(l) _(m) )  (7)

GA may be applied after serving signal cancellation. The presentdisclosure provides an ML solution after GA (ML-GA), and provides afurther approximation over the ML-GA solution for reducing complexityand providing a feasible solution for a hardware implementation.

At 111, hypotheses that maximize the likelihood metrics are determinedand the traffic to pilot ration (TPR) is determined.

With the above GA for R_(k)=E{y_(k)y_(k) ^(H))}, Equation (8) is asfollows:R _(k) =G _(k) ^(S) P ^(S)(P ^(S))^(H)(G _(k) ^(S))^(H)+ρ_(I) ² G _(k)^(I) P ^(I,l) ^(I,p) (p ^(I,l) ^(I,p) )^(H)(G _(k) ^(I))^(H)+σ² I  (8)

If G_(k) ^(S), P^(S), G_(k) ^(I) and σ² are given, R_(k) is a functionof) ρ_(I) ²P^(I,l) ^(I,p) (P^(I,l) ^(I,p) )^(H). For different rank 1precoding indices, p^(I,1,p) ¹ (P^(I,1,p) ¹ )^(H)≠P^(I,1,p) ¹ )^(H) forp₁≠p₂. For both SFBC and rank 2, P^(I,l) ^(I) ^(,p)(P^(I,l) ^(I)^(,p))^(H)=½I_(N) _(r) .

At 113, the present system determines whether the received signal or theserving-signal-cancelled received signal is of rank 1. At 113, rank 1and rank 2/SFBC are differentiated.

At 115, if the present system determines at 113 that the rank of thereceived signal or the serving-signal-cancelled received signal is rank1, rank 1 PMI is identified and TPR, rank, and PMI are returned.

A cmi parameter may be defined where a cmi set is defined as cmi∈{0,1,2,3,4} with cmi=i (for i ∈ {0,1,2,3}) corresponding to rank 1 witha precoding index of p=i, and cmi=4 corresponding to rank 2 and SFBC,where SFBC may not be distinguished from rank 2, and no information maybe provided regarding a rank 2 precoding index.

According to an embodiment of the present disclosure, the present systemprovides joint TPR and CMI detection as a first step of sequential blinddetection. If cmi is identified as cmi≠4, rank and precoding are known.However, if cmi is identified as cmi=4, then SFBC and rank 2 must bedifferentiated.

At 117, if the present system does not determine that the rank of thereceived signal or the serving-signal-cancelled received signal is rank1, the present system determines whether transmit diversity is presentin the received signal or the serving-signal-cancelled received signal.That is, if transmit diversity is present then SFBC is detected.Otherwise, the rank of the received signal or theserving-signal-cancelled received signal is rank 2. In an embodiment ofthe present disclosure, a blind SFBC detection method may be applied todifferentiate rank 2 from SFBC.

If SFBC is detected at 117, then the present system returns todetermining a PMI of the received signal or the serving-signal-cancelledreceived signal that concerns SFBC and returning TPR, rank, and PMI at115. If SFBC is not detected at 117, the present system determines thatthe rank is 2 at 119.

If rank 2 is determined at 119, then the present system returns todetermining a PMI for the received signal or theserving-signal-cancelled received signal of rank 2 and returning TPR,rank, and PMI at 115.

With GA, a likelihood metric to be maximized may be as in Equation (9)as follows:

ρ I , cmi = ∏ k = 1 K ⁢ 1  R k ⁡ ( ρ I , cmi )  ⁢ e - y k H ⁢ R k - 1 ⁡ ( ρI , cmi ) ⁢ y k , ( 9 )where |R_(k)(ρ_(I), cmi)| denotes a determinant of matrix R_(k)(ρ_(I),cmi). If Equation (10) is defined as follows:

M ρ I , cmi = ⁢ - log ⁡ ( ρ I , cmi ) = ⁢ ∑ k = 1 K ⁢ y k H ⁢ R k - 1 ⁡ ( ρ I, cmi ) ⁢ y k + log ⁡ (  R k ⁡ ( ρ I , cmi )  ) = ⁢ ∑ k = 1 K ⁢ trace ⁡ ( yk ⁢ y k H ⁢ R k - 1 ⁡ ( ρ I , cmi ) ) + log ⁡ (  R k ⁡ ( ρ I , cmi )  ) , (10 )where trace(ABC)=trace(CAB), then an ML joint identification of (ρ_(I),cmi) is obtained as in Equation (11) as follows:({circumflex over (ρ)}_(I) ,

l)=argmin_(ρ) _(I) _(,cmi) M _(ρ) _(I) _(,cmi)  (11)

Furthermore, if Equations (12)-(15) are defined as follows:

$\begin{matrix}\begin{matrix}{R_{k}^{S} = {G_{k}^{S}{P^{S}\left( P^{S} \right)}^{H}\left( G_{k}^{S} \right)^{H}}} \\{{= \begin{bmatrix}r_{k,00}^{S} & r_{k,01}^{S} \\r_{k,10}^{S} & r_{k,11}^{S}\end{bmatrix}},}\end{matrix} & (12) \\\begin{matrix}{{R_{k}^{I}({cmi})} = {G_{k}^{I}{P^{I,l_{I},p}\left( P^{I,l_{I},p} \right)}^{H}\left( G_{k}^{I} \right)^{H}}} \\{{= \begin{bmatrix}{r_{k,00}^{I}({cmi})} & {r_{k,01}^{I}({cmi})} \\{r_{k,10}^{I}({cmi})} & {r_{k,11}^{I}({cmi})}\end{bmatrix}},}\end{matrix} & (13) \\{{D_{k}^{S} = \begin{bmatrix}r_{k,11}^{S} & {- r_{k,01}^{S}} \\{- r_{k,10}^{S}} & r_{k,00}^{S}\end{bmatrix}},{and}} & (14) \\{{{D_{k}^{I}({cmi})} = \begin{bmatrix}{r_{k,11}^{I}({cmi})} & {- {r_{k,01}^{I}({cmi})}} \\{- {r_{k,10}^{I}({cmi})}} & {r_{k,00}^{I}({cmi})}\end{bmatrix}},} & (15)\end{matrix}$then R_(k) ⁻¹(ρ_(I),cmi) may be described as in Equation (16) asfollows:

$\begin{matrix}{{R_{k}^{- 1}\left( {\rho_{I},{cmi}} \right)} = {\frac{D_{k}^{S} + {\rho_{I}^{2}{D_{k}^{I}({cmi})}} + {\sigma^{2}I}}{{R_{k}\left( {\rho_{I},{cmi}} \right)}}.}} & (16)\end{matrix}$

In the presence of a serving signal and using two CRS antenna ports,Equation (17) is obtained as follows:

$\begin{matrix}{M_{\rho_{I},{cmi}} = {{\sum\limits_{k = 1}^{K}\frac{{{trace}\left( {y_{k}{y_{k}^{H}\left( {D_{k}^{S} + {\sigma^{2}I}} \right)}} \right)} + {\rho_{I}^{2}{{trace}\left( {y_{k}y_{k}^{H}{D_{k}^{I}({cmi})}} \right)}}}{{R_{k}\left( {\rho_{I},{cmi}} \right)}}} + {\log\left( {{R_{k}\left( {\rho_{I},{cmi}} \right)}} \right)}}} & (17)\end{matrix}$

If a serving signal is cancelled and two CRS antenna ports are used,Equation (18) is obtained as follows:

$\begin{matrix}{{M_{\rho_{I},{cmi}} = {{\sum\limits_{k = 1}^{K}\frac{{\sigma^{\prime^{2}}{{trace}\left( {y_{k}^{\prime}y_{k}^{\prime^{H}}} \right)}} + {\rho_{I}^{2}{{trace}\left( {y_{k}y_{k}^{H}{D_{k}^{\prime^{I}}({cmi})}} \right)}}}{{R_{k}^{\prime}\left( {\rho_{I},{cmi}} \right)}}} + {\log\left( {{R_{k}^{\prime}\left( {\rho_{I},{cmi}} \right)}} \right)}}},} & (18)\end{matrix}$where y′_(k) is given in Equation (4) above and R′_(k)(ρ_(I), cmi)=ρ_(I)²W_(k)G_(k) ^(I)P^(I,l) ^(I) ^(,p)(p^(I,l) ^(I) ^(,p))^(H)(G_(k)^(I))^(H)W_(k) ^(H)+σ′²I.

According to an embodiment of the present disclosure, TPR detection forone CRS antenna port is provided. For one CRS antenna port, no precodingis applied, and only ρ_(I) may be identified. Therefore, a metric as inEquation (19) may be as follows:

$\begin{matrix}{{M_{\rho_{I}} = {{\sum\limits_{k = 1}^{K}\frac{{{trace}\left( {y_{k}{y_{k}^{H}\left( {D_{k}^{S} + {\sigma^{2}I}} \right)}} \right)} + {\rho_{I}^{2}{{trace}\left( {y_{k}y_{k}^{H}D_{k}^{I}} \right)}}}{{R_{k}\left( \rho_{I} \right)}}} + {\log\left( {{R_{k}\left( \rho_{I} \right)}} \right)}}},} & (19)\end{matrix}$where D_(k) ^(I) is known (not a function of precoding) and ρ_(I) may beidentified.

The computational complexity of M_(ρ) _(I) _(,cmi) in Equations (17) and(18) above, and M_(ρ) _(I) in Equation (19) is still high sincelog(|R_(k)(ρ_(I),cmi)|) must be determined, division by|R_(k)(ρ_(I),cmi)| must be performed for each RE of a given RB, for eachpair of (ρ_(I),cmi), where (ρ_(I),cmi) represents one possiblehypothesis. In addition, there are 15 possible hypotheses per RB (e.g.,3 possibilities for ρ_(I) and 5 possibilities for cmi).

In an embodiment of the present disclosure, a further approximation overM_(ρ) _(I) _(, cmi) is provided (e.g., a further approximation overML-GA), which reduces hardware complexity.

Due to Jensen's inequality, Equation (20) is as follows:

$\begin{matrix}{{\sum\limits_{k = 1}^{K}{\log\left( {{R_{k}\left( {\rho_{I},{cmi}} \right)}} \right)}} \leq {K\;{{\log\left( \frac{{R_{k}\left( {\rho_{I},{cmi}} \right)}}{K} \right)}.}}} & (20)\end{matrix}$

The inequality in Equation (20) above becomes an equality for staticchannels, i.e., R_(k) ₁ (ρ_(l),cmi)=R_(k) ₂ (ρ_(I),cmi) for all k₁ andk₂. Furthermore,

$\sum\limits_{k = 1}^{K}\frac{a_{k}}{b_{k}}$may be approximated as in Equation (21) as follows:

$\begin{matrix}{{\sum\limits_{k = 1}^{K}\frac{a_{k}}{b_{k}}} \approx {\frac{\sum\limits_{k = 1}^{K}a_{k}}{\sum\limits_{k = 1}^{K}\frac{b_{k}}{K}}.}} & (21)\end{matrix}$

The approximation in Equation (21) above becomes exact for staticchannel cases. By substituting Equations (20) and (21) intoEquation(17), Equation (22) is obtained as follows:

$\begin{matrix}{M_{\rho_{I},{cmi}} \approx {\frac{{\sum\limits_{k = 1}^{K}{{trace}\left( {y_{k}{y_{k}^{H}\left( {D_{k}^{S} + {\sigma^{2}I}} \right)}} \right)}} + {\rho_{I}^{2}{{trace}\left( {y_{k}y_{k}^{H}{D_{k}^{I}({cmi})}} \right)}}}{\sum\limits_{k = 1}^{K}\frac{{R_{k}\left( {\rho_{I},{cmi}} \right)}}{K}} + {K\;{{\log\left( \frac{\sum\limits_{k = 1}^{K}{{R_{k}\left( {\rho_{I},{cmi}} \right)}}}{K} \right)}.}}}} & (22)\end{matrix}$

The above approximation reduces the required number of divisions andlogarithm calculations by a factor of K, where K is a number of REs inat least one RB.

Calculation complexity may be reduced further in the calculation of|R_(k)(ρ_(l),cmi)|. If |R_(k)(ρ_(I),cmi)| for each hypothesis isdirectly calculated, then a calculation per RE is for 15 hypotheses(e.g., 5 possibilities for cmi and 3 possibilities for ρ_(I), where thethree possible ρ_(I) values are signaled to a UE). If R_(k) ^(S) andR_(k) ^(I)(cmi) are given, Equation (23) as follows may be determinedfirst:R _(k)(ρ_(I),cmi)=R _(k) ^(S)+ρ_(I) ² R _(k) ^(I)(cmi)+σ² I,  (23)where, for each (ρ_(I),cmi) pair, 4 multiplications per hypothesis arerequired, and a total of 60 multiplications and 15 2×2 determinationsare required per RE.

A lower complexity calculation of |R_(k)(ρ_(I),cmi)| is described inEquation (24) as follows:

$\begin{matrix}{{{{R_{k}\left( {\rho_{I},{cmi}} \right)}} = {{{R_{k}^{S} + {\rho_{I}^{2}{R_{k}^{I}({cmi})}} + {\sigma^{2}I}}} = {{{R_{k}^{S} + {\sigma^{2}I}}} + {\rho_{I}^{4}{{R_{k}^{I}({cmi})}}} + {\rho_{I}^{2}\left( {{{A_{k}({cmi})}}{{B_{k}({cmi})}}} \right)}}}}\mspace{20mu}{where}\mspace{20mu}{{{A_{k}({cmi})} = \begin{bmatrix}{r_{k,00}^{S} + \sigma^{2}} & r_{k,01}^{S} \\{r_{k,10}^{I}({cmi})} & {r_{k,11}^{I}({cmi})}\end{bmatrix}},\mspace{20mu}{{and}\mspace{14mu}{where}}}\mspace{20mu}{{B_{k}({cmi})} = {\begin{bmatrix}{r_{k,00}^{I}({cmi})} & {r_{k,01}^{I}({cmi})} \\r_{k,10}^{S} & {r_{k,11}^{S} + \sigma^{2}}\end{bmatrix}.}}} & (24)\end{matrix}$

For cmi ∈ {0,1,2,3}, R_(k) ^(I)(cmi) is a rank 1 matrix, then |R_(k)^(I)(cmi)|0 for cmi ∈ {0,1,2,3} and only |R_(k) ^(I)(cmi)| may bedetermined for cmi=4. Therefore, for Σ_(k=1) ^(K)|R_(k)(ρ_(I),cmi)|,Equation (25) is as follows:

$\begin{matrix}{{\sum\limits_{k = 1}^{K}{{R_{k}\left( {\rho_{I},{cmi}} \right)}}} = {{\sum\limits_{k = 1}^{K}{{R_{k}^{S} + {\sigma^{2}I}}}} + \left\{ \begin{matrix}{\rho_{I}^{2}{\sum\limits_{k = 1}^{K}\left( {{{A_{k}({cmi})}} + {{B_{k}({cmi})}}} \right)}} & {{cmi} \in \left\{ {0,1,2,3} \right\}} \\{{\rho_{I}^{4}{\sum\limits_{k = 1}^{K}{{R_{k}^{I}({cmi})}}}} + {\rho_{I}^{2}{\sum\limits_{k = 1}^{K}\left( {{{A_{k}({cmi})}} + {{B_{k}({cmi})}}} \right)}}} & {{cmi} = 4}\end{matrix} \right.}} & (25)\end{matrix}$

To calculate Σ_(k=1) ^(K)|R_(k)(ρ_(I),cmi)|, 12 2×2 matrix determinantsper RE are required, and in total, per RB, 12K 2×2 matrix determinantsand 6 multiplications are required.

If a 2×2 matrix determinant calculation requires two multiplications,|R_(k)(ρ_(i),cmi)| is calculated directly per RE, Σ_(k=1)^(K)|R_(k)(ρ_(I),cmi)| is calculated, and 90 multiplications per RE anda total of 90K multiplications per RB are required. However, Equation(25) above may be used so that only 24 multiplications per RE and atotal of 24K+6 multiplications per RB are required.

According to an embodiment of the present disclosure, a furtherapproximation over ML-GA is applied for serving signal cancellation inthe calculation of Equation (18) above where |R′_(k)(ρ_(I),cmi)|=|ρ_(I)²W_(k)G_(k) ^(I)P^(I,l) ^(I) _(,p)(p^(I,l) ^(I) ^(,p))^(H)(G_(k)^(I))^(H)W_(k) ^(H)+σ′²I| is calculated for 15 possible hypothesis.Therefore, Equation (26) is as follows:

$\begin{matrix}{{\sum\limits_{k = 1}^{K}{{R_{k}^{\prime}\left( {\rho_{I},{cmi}} \right)}}} = {{K\;\sigma^{\prime 4}} + \left\{ \begin{matrix}{\rho_{I}^{2}\sigma^{\prime 2}{\sum\limits_{k = 1}^{K}\left( {{r_{k,11}^{\prime}{\,^{I}({cmi})}} + {r_{k,00}^{\prime}{\,^{I}({cmi})}}} \right)}} & {{cmi} \in \left\{ {0,1,2,3} \right\}} \\{{\rho_{I}^{4}{\sum\limits_{k = 1}^{K}{{R_{k}^{\prime}{\,^{I}({cmi})}}}}} + {\rho_{I}^{2}\sigma^{\prime 2}{\sum\limits_{k = 1}^{K}\left( {{r_{k,11}^{\prime}{\,^{I}({cmi})}} + {r_{k,00}^{\prime}{\,^{I}({cmi})}}} \right)}}} & {{cmi} = 4}\end{matrix} \right.}} & (26)\end{matrix}$

From Equation (26) above, calculating Σ_(k=1) ^(K)|R′_(k)(ρ_(I),cmi)|only requires one 2×2 matrix determinant per RE, and a total of K 2×2matrix determinants and 9 multiplications per RB.

If a 2×2 matrix determinant calculation requires two multiplications,|R′_(k)(ρ_(I),cmi)| is calculated directly per RE, Σ_(k=1)^(K)|R_(k)(ρ_(I),cmi)| is calculated, and 90 multiplications per RE anda total of 90K multiplications per RB are required. However, Equation(26) above may be used so that only 2 multiplications per RE and a totalof 2K+9 multiplications per RB are required. For serving signalcancellation, whitening over the residual serving signal and noise maybe applied.

The GA method and the GA method with further approximation providebetter TPR and joint TPR-CMI blind detection performance than aprojection method. In addition, the GA method has a performance that isclose to that of the GA method with further approximation.

According to an embodiment of the present disclosure, rank 2 precodingidentification is provided. If the received signal is rank 2, TPR isknown, the serving signal is cancelled, and Equation (27) is as follows:y _(k)=ρ_(I) ² G _(k) ^(I) P ^(I,2,p) x _(k) +n _(k).  (27)

A minimum mean square error (MMSE) filter W_(k)=(ρ_(I) ⁴G_(k) ^(I) ^(H)G_(k) ^(I)+σ²I)⁻¹ ρ_(I) ²G_(k) ^(I) ^(H) may be applied to obtainEquation (28) as follows:

$\begin{matrix}{{{y_{k}^{\prime} = {{W_{k}y_{k}} = {{P^{I,2,p}x_{k}} + n_{k}^{\prime}}}},{where}}{P^{I,2,0} = {{{\frac{1}{2}\begin{bmatrix}1 & 1 \\{- 1} & 1\end{bmatrix}}\mspace{14mu}{and}\mspace{14mu} P^{I,2,1}} = {{\frac{1}{2}\begin{bmatrix}1 & 1 \\j & {- j}\end{bmatrix}}.}}}} & (28)\end{matrix}$

If β_(k,I)=Re{y′_(k,1)y′_(k,2)*} are β_(k,Q)=Im{y′_(k,1)y′_(k,2)*} aredefined, Equations (29) and (30) are obtained as follows:

$\begin{matrix}{\beta_{I} = \left\{ \begin{matrix}{{{Re}\left\{ {{\left( {x_{k,1} + x_{k,2}} \right)\left( {{- x_{k,1}} + x_{k,2}} \right)^{*}} + Z_{k}} \right\}} = {{x_{k,2}}^{2} - {x_{k,1}}^{2} + Z_{k,I}}} & {p = 0} \\{{{Re}\left\{ {{\left( {x_{k,1} + x_{k,2}} \right)\left( {{jx}_{k,1} - {jx}_{k,2}} \right)^{*}} + Z_{k}} \right\}} = {{{- 2}\;{Im}\left\{ {x_{k,1}x_{k,2}^{*}} \right\}} + Z_{k,1}}} & {p = 1}\end{matrix} \right.} & (29) \\{\mspace{79mu}{and}} & \; \\{\beta_{Q} = \left\{ {\begin{matrix}{{{Im}\left\{ {{\left( {x_{k,1} + x_{k,2}} \right)\left( {{- x_{k,1}} + x_{k,2}} \right)^{*}} + Z_{k}} \right\}} = {{2\;{Im}\left\{ {x_{k,1}x_{k,2}^{*}} \right\}} + Z_{k,Q}}} & {p = 0} \\{{{Im}\left\{ {{\left( {x_{k,1} + x_{k,2}} \right)\left( {{jx}_{k,1} - {jx}_{k,2}} \right)^{*}} + Z_{k}} \right\}} = {{x_{k,2}}^{2} - {x_{k,1}}^{2} + Z_{k,Q}}} & {p = 1}\end{matrix}.} \right.} & (30)\end{matrix}$

For both p=0 and p=1, with QAM signaling, E{β_(k,I)}=E{β_(k,Q)}=0

Therefore, there is no linear operation over β_(k,I) and β_(k,Q) whichmay reveal the rank 2 precoding index. However, for a given p, β_(k,I)and β_(k,Q) have different distributions. Therefore, with somenon-linear operation f(.), with a property thatE{f(β_(k,I))}≠E{f(β_(k,Q))}, a rank 2 precoding index may be identifiedbased on Equations (31) and (32) as follows:

$\begin{matrix}{M_{I} = {{\frac{1}{K}{\sum\limits_{k = 1}^{K}{f\left( \beta_{k,I} \right)}}} \approx {E\left\{ {f\left( \beta_{k,I} \right)} \right\}}}} & (31) \\{and} & \; \\{M_{Q} = {{\frac{1}{K}{\sum\limits_{k = 1}^{K}{f\left( \beta_{k,Q} \right)}}} \approx {E{\left\{ {f\left( \beta_{k,Q} \right)} \right\}.}}}} & (32)\end{matrix}$

Table 2 below illustrates a distribution of |x₂|²−|x₁|² and Im{x₁x*₂}for QPSK, 16 QAM and 64 QAM.

TABLE 2 Modulati Possible on order Values Corresponding ProbabilitiesQPSK |x₂|² − |x₁|² 0 1 Im{x₁x₂ ^(*)} {−1, 1}$\quad\left\{ {\frac{1}{2},\frac{1}{2}} \right\}$ 16QAM |x₂|² − |x₁|²{−1.6, −0.8, 0, 0.8, 1.6}$\quad\left\{ {\frac{1}{16},\frac{1}{4},\frac{3}{8},\frac{1}{4},\frac{1}{16}} \right\}$Im{x₁x₂ ^(*)} {−3.6, −2.4, −2, −1.6, −1.2, −0.8, −0.4, 0, 0.4, 0.8, 1.2,1.6, 2.2, 2.4, 3.6} $\quad\begin{Bmatrix}{\frac{1}{64},\frac{1}{16},\frac{1}{32},\frac{1}{32},\frac{1}{8},} \\{\frac{1}{16},\frac{5}{64},\frac{3}{16},\frac{5}{64},\frac{1}{16},} \\{\frac{1}{8},\frac{1}{32},\frac{1}{32},\frac{1}{16},\frac{1}{64}}\end{Bmatrix}$ 64QAM |x₂|² − |x₁|² {−2.29, −2.10, −1.91, {16, 32, 16,64, 96, 64, −1.72, −1.53, −, −1.15, 224, 224, 144, 384, −0.96, −0.77,−0.58, 272, 256, 512, 256, −0.39, −, 0, 0.19, 0.38, 272, 384 144, 224,2, 0.57, 0.76, 0.95, 64, 96, 64, 16, 32, 1.14, 1.33, 1.52, 1.71,16}/4096 1.90, 2.09, 2.28} Im{x₁x₂ ^(*)} 71 different possibilities forIm{x₁x₂ ^(*)} under 64QAM modulation

For the non-linear operation f(.), two different operationsf(β_(k,I))=|β_(k,I)| and f(β_(k,I))=|β_(k,I)|² may be used, but thepresent disclosure is not limited thereto. Other non-linear operationsmay also be used. Table 3 below illustrates a comparison ofE{f(|x₂|²−|x₁|²)} and E{f(Im{x₁x₂*})} with f(α)=|α| and f(α)=|α|² fordifferent modulation orders. Table 3 below shows that these non-linearoperations, E{f(β_(k,I))}≠E{f(β_(k,Q))} enable identification of a rank2 precoding index.

TABLE 3 Modulation order E{| · |} E{| · |²} QPSK |x₂|² − |x₁|² 0 0Im{x₁x₂*} 1 1 16QAM |x₂|² − |x₁|² 0.6 0.64 Im{x₁x₂*} 1.1 2 64QAM |x₂|² −|x₁|² 0.694 0.7619 Im{x₁x₂*} 1.1116 2

Based on the property of the above non-linear functions, the precodingidentification rule may be defined as in Equation (33) as follows:

$\begin{matrix}{\hat{p} = \left\{ \begin{matrix}0 & {M_{Q} > M_{I}} \\1 & {M_{Q} < M_{I}}\end{matrix} \right.} & (33)\end{matrix}$where M_(I) and M_(Q) are given in Equations (31) and (32) above.

FIG. 2 is a block diagram of an apparatus 200 for blind detection ofinterference patterns in an LTE system using GA over both interferingand serving signals, according to an embodiment of the presentdisclosure.

Referring to FIG. 2, the apparatus 200 includes an antenna 201, atransceiver 203, and a processor 205.

The antenna 201 receives a signal, where the signal may include aserving signal, at least one interfering signal, or a combinationthereof.

The transceiver 203 includes an input connected to the antenna 201 forreceiving the received signal, and an output.

The processor 205 includes an input connected to the output of thetransceiver 203 and is configured to cancel a serving signal in thereceived signal or not. If a serving signal is cancelled from thereceived signal then a processor 205 is further configured to determinea sampled covariance matrix of the serving-signal-cancelled receivedsignal. If a serving signal is not cancelled from the received signalthen the processor is further configured to determine a sampledcovariance matrix of the received signal.

The processor 205 is further configured to determine likelihood metricsfor hypotheses on interference signal rank, precoding matrix, and powerwith GA on interfering signals.

The processor 205 is further configured to determine hypotheses thatmaximize the likelihood metrics.

After determining the hypotheses that maximize likelihood metrics, theprocessor 205 is further configured to determine whether the receivedsignal or the serving-signal-cancelled received signal is of rank 1.

If the processor 205 determines that the rank of the received signal orthe serving-signal-cancelled received signal is rank 1, the processor205 is further configured to identify a TPR, and detect a rank 1precoding index based on the above GA.

If the processor 205 determines that the rank of the received signal orthe serving-signal-cancelled received signal is not rank 1, theprocessor 205 is further configured to determine whether transmitdiversity is present in the received signal or theserving-signal-cancelled received signal. That is, if transmit diversityis present then SFBC is detected. Otherwise, the rank of the receivedsignal or the serving-signal-cancelled received signal is rank 2. In anembodiment of the present disclosure, a blind SFBC detection method maybe applied to differentiate rank 2 from SFBC.

If SFBC is detected, then the processor 205 is further configured todetermine a precoding index and power index of interference of thereceived signal or the serving-signal-cancelled received signal thatconcerns SFBC. Otherwise, rank 2 is determined.

If rank 2 is determined, then the processor 205 is further configured todetermine a precoding index and a power index of interference for thereceived signal or the serving-signal-cancelled received signal of rank2.

In an embodiment of the present disclosure, a further approximation overM_(ρ) _(I) _(,cmi) is provided (e.g., a further approximation overML-GA), which reduces hardware complexity.

The approximation as shown in Equation (22) above, which reduces therequired number of divisions and logarithm calculations by a factor ofK, where K is a number of REs in at least one RB.

Calculation complexity may be reduced further in the calculation of|R_(k)(ρ_(I),cmi)|. A lower complexity calculation of |R_(k)(ρ_(I),cmi)|is described in Equation (24) above.

For cmi ∈ {0,1,2,3}, R_(k) ^(I)(cmi) is a rank 1 matrix, then |R_(k)^(I)(cmi)|=0 for cmi ∈ {0,1,2,3} and only |R_(k) ^(I)(cmi)| may bedetermined for cmi=4. Therefore, for Σ_(k=1) ^(K)|R_(k)(ρ_(I),cmi)|,Equation (25) is as described above.

To calculate Σ_(k=1) ^(K)|R_(k)(ρ_(I),cmi)|, 12 2×2 matrix determinantsper RE are required, and in total, per RB, 12K 2×2 matrix determinantsand 6 multiplications are required.

If a 2×2 matrix determinant calculation requires two multiplications,|R_(k)(ρ_(I),cmi)| is calculated directly per RE, Σ_(k=1)^(K)|R_(k)(ρ_(I),cmi)| is calculated, and 90 multiplications per RE anda total of 90K multiplications per RB are required. However, Equation(25) above may be used so that only 24 multiplications per RE and atotal of 24K+6 multiplications per RB are required.

According to an embodiment of the present disclosure, a furtherapproximation over ML-GA is applied for serving signal cancellation inthe calculation of Equation (18) above where |R′_(k)(ρ_(I),cmi)|=|ρ_(I)²W_(k)G_(k) ^(I)P^(I,l) ^(I) ^(p)(P^(I,l) ^(I) ^(,p))^(H)(G_(k)^(I))^(H)W_(k) ^(H)+σ′²I| is calculated for 15 possible hypothesis.Therefore, Equation (26) is as described above.

From Equation (26) above, calculating Σ_(k=1) ^(K)|R′_(k)(ρ_(I),cmi)|only requires one 2×2 matrix determinant per RE, and a total of K 2×2matrix determinants and 9 multiplications per RB.

If a 2×2 matrix determinant calculation requires two multiplications,|R′_(k)(ρ_(I),cmi)| is calculated directly per RE, Σ_(k=1)^(K)|R_(k)(ρ_(I),cmi)| is calculated, and 90 multiplications per RE anda total of 90K multiplications per RB are required. However, Equation(26) above may be used so that only 2 multiplications per RE and a totalof 2K+9 multiplications per RB are required. For serving signalcancellation, whitening over the residual serving signal and noise maybe applied.

According to an embodiment of the present disclosure, rank 2 precodingidentification is provided. If the received signal is rank 2, TPR isknown, the serving signal is cancelled. With some non-linear operationf(.), with a property that E{f(β_(k,I))}≠E{f(β_(k,Q))}, a rank 2precoding index may be identified based on Equations (31) and (32)described above. For the non-linear operation f(.), two differentoperations f(β_(k,I))=|β_(k,I)| and f(β_(k,I))=|β_(k,I)|² may be used,but the present disclosure is not limited thereto. Other non-linearoperations may also be used.

Based on the property of the above non-linear functions, the precodingidentification rule may be defined as in Equation (33) described above.

Although certain embodiments of the present disclosure have beendescribed in the detailed description of the present disclosure, thepresent disclosure may be modified in various forms without departingfrom the scope of the present disclosure. Thus, the scope of the presentdisclosure shall not be determined merely based on the describedembodiments, but rather determined based on the accompanying claims andequivalents thereto.

What is claimed is:
 1. A method, comprising: receiving a signalincluding a serving signal and an interference signal; applying aGaussian approximation (GA) on a serving signal and the interferencesignal; determining, for one or more hypotheses, likelihood metrics fora rank of the interference signal, a precoding matrix index, and poweron the GA-applied interference signal, wherein each hypothesis is aunique combination of a traffic to pilot ratio (TPR) from one or moreTPRs of the interference signal and a covariance matrix index (CMI) fromone or more CMIs; and determining a TPR from at least one of thehypotheses that maximize the likelihood metrics.
 2. The method of claim1, further comprising: determining, jointly, a maximum likelihood (ML)solution of rank, the TPR, and a precoding matrix index on theGA-applied serving signal and the GA-applied interference signal; anddetermining, sequentially, the rank of the interference signal based onthe jointly determined ML solution.
 3. The method of claim 2, wherein acovariance matrix is determined on the received signal after the servingsignal is cancelled from the received signal.
 4. The method of claim 2,further comprising: determining if the rank is 1; if the rank is not 1then determining if transmit diversity is present; if the transmitdiversity is not present then determining that the rank is 2;determining the precoding matrix index if the rank is 1, the transmitdiversity is present, or if the rank is 2; and returning thedeterminations of the TPR, the rank, and the precoding matrix index. 5.The method of claim 3, further comprising: determining if the rank is 1;if the rank is not 1 then determining if transmit diversity is present;if the transmit diversity is not present then determining that the rankis 2; determining the precoding matrix index if the rank is 1, thetransmit diversity is present, or if the rank is 2; and returning thedeterminations of the TPR, the rank, and the precoding matrix index. 6.The method of claim 4, wherein the ML solution of rank, TPR, andprecoding matrix index is determined for at least one cell-specificreference signal (CRS) antenna port.
 7. The method of claim 5, whereinthe ML solution of rank, TPR, and precoding matrix index is determinedfor at least one cell-specific reference signal (CRS) antenna port. 8.The method of claim 6, wherein the likelihood metric is one of:${M_{\rho_{I}} = {{\sum\limits_{k = 1}^{K}\frac{{{trace}\left( {y_{k}{y_{k}^{H}\left( {D_{k}^{S} + {\sigma^{2}I}} \right)}} \right)} + {\rho_{I}^{2}{{trace}\left( {y_{k}y_{k}^{H}D_{k}^{I}} \right)}}}{{R_{k}\left( \rho_{I} \right)}}} + {\log\left( {{R_{k}\left( \rho_{I} \right)}} \right)}}};$$M_{\rho_{I}} = {\frac{{\underset{k = 1}{\sum\limits^{K}}{{trace}\left( {y_{k}{y_{k}^{H}\left( {D_{k}^{S} + {\sigma^{2}I}} \right)}} \right)}} + {\rho_{I}^{2}{{trace}\left( {y_{k}y_{k}^{H}D_{k}^{I}} \right)}}}{\sum\limits_{k = 1}^{K}\frac{{R_{k}\left( \rho_{I} \right)}}{K}} + {K\;{\log\left( \frac{\sum\limits_{k = 1}^{K}{{R_{k}\left( \rho_{I} \right)}}}{K} \right)}}}$${M_{\rho_{I,{cmi}}} = {{\sum\limits_{k = 1}^{K}\frac{{{trace}\left( {y_{k}{y_{k}^{H}\left( {D_{k}^{S} + {\sigma^{2}I}} \right)}} \right)} + {\rho_{I}^{2}{{trace}\left( {y_{k}y_{k}^{H}{D_{k}^{I}({cmi})}} \right)}}}{{R_{k}\left( {\rho_{I},{cmi}} \right)}}} + {\log\left( {{R_{k}\left( {\rho_{I},{cmi}} \right)}} \right)}}};{or}$${M_{\rho_{I},{cmi}} \approx {\frac{{\underset{k = 1}{\sum\limits^{K}}{{trace}\left( {y_{k}{y_{k}^{H}\left( {D_{k}^{S} + {\sigma^{2}I}} \right)}} \right)}} + {\rho_{I}^{2}{{trace}\left( {y_{k}y_{k}^{H}{D_{k}^{I}({cmi})}} \right)}}}{\sum\limits_{k = 1}^{K}\frac{{R_{k}\left( {\rho_{I},{cmi}} \right)}}{K}} + {K\;{\log\left( \frac{\sum\limits_{k = 1}^{K}{{R_{k}\left( {\rho_{I},{cmi}} \right)}}}{K} \right)}}}},$where M_(ρ) _(I) represents the metric in one CRS antenna port case andM_(ρ) _(I) _(,cmi) represent the metric in two CRS antenna port case,y_(k)=H_(k) ^(S)x_(k) ^(S)+ρ_(I)H_(k) ^(I)x_(k) ^(I)+n_(k), H_(k) ^(m)represents an effective channel matrix from a serving evolved node B(eNB) to a user equipment (UE) for m=S and from an interfering cell tothe UE for m=I, where ρ_(I) represents a TPR of an interfering signal,x_(k) ^(m)=[x_(k) ^(m,1), . . . , x_(k) ^(m,l) ^(m) ]^(T) is a l_(m)×1transmit signal vector, l_(m) indicates a number of transmission layers,n_(k) is an additive white Gaussian noise (AWGN) vector with covarianceE{n_(k)n_(k) ^(H)}=σ²I, K is a integer, |R_(k)(ρ_(I))| denotes adeterminant of matrix R_(k)(ρ_(I))=R_(k) ^(S)+ρ_(I) ²R_(k) ^(I)+σ²I,$R_{k}^{S} = \begin{bmatrix}r_{k,00}^{S} & r_{k,01}^{S} \\r_{k,10}^{S} & r_{k,11}^{S}\end{bmatrix}$ $R_{k}^{I} = \begin{bmatrix}r_{k,00}^{I} & r_{k,01}^{I} \\r_{k,10}^{I} & r_{k,11}^{I}\end{bmatrix}$ ${D_{k}^{S} = \begin{bmatrix}r_{k,11}^{S} & {- r_{k,01}^{S}} \\{- r_{k,10}^{S}} & r_{k,00}^{S}\end{bmatrix}},{and}$ ${D_{k}^{I} = \begin{bmatrix}r_{k,11}^{I} & {- r_{k,01}^{I}} \\{- r_{k,10}^{I}} & r_{k,00}^{I}\end{bmatrix}},$ and |R_(k)(ρ_(I), cmi)| denotes a determinant of matrixR_(k)(ρ_(I), cmi)=R_(k) ^(S)+ρ_(I) ²R_(k) ^(I)(cmi)+σ²I, where$\begin{matrix}{{R_{k}^{I}({cmi})} = {G_{k}^{I}{P^{I,l_{I},p}\left( P^{I,l_{I},p} \right)}^{H}\left( G_{k}^{I} \right)^{H}}} \\{{= \begin{bmatrix}{r_{k,00}^{I}({cmi})} & {r_{k,01}^{I}({cmi})} \\{r_{k,10}^{I}({cmi})} & {r_{k,11}^{I}({cmi})}\end{bmatrix}},}\end{matrix}$ and ${{D_{k}^{I}({cmi})} = \begin{bmatrix}{r_{k,11}^{I}({cmi})} & {- {r_{k,01}^{I}({cmi})}} \\{- {r_{k,10}^{I}({cmi})}} & {r_{k,00}^{I}({cmi})}\end{bmatrix}},$ then R_(k) ⁻¹(ρ_(I), cmi) is as follows:${{R_{k}^{- 1}\left( {\rho_{I},{cmi}} \right)} = \frac{D_{k}^{S} + {\rho_{I}^{2}{D_{k}^{I}({cmi})}} + {\sigma^{2}I}}{{R_{k}\left( {\rho_{I},{cmi}} \right)}}},$wherein cmi ∈{0,1,2,3,4} with cmi=i (for i ∈{0,1,2,3}) corresponding torank 1 with a precoding index of p=i, and cmi=4 corresponding to rank 2and SFBC, and wherein there are 5 possible hypotheses for cmi and 3possible hypotheses for ρ_(I).
 9. The method of claim 7, wherein thelikelihood metric is one of:${M_{\rho_{I}} = {{\sum\limits_{k = 1}^{K}\frac{{{trace}\left( {y_{k}{y_{k}^{H}\left( {D_{k}^{S} + {\sigma^{2}I}} \right)}} \right)} + {\rho_{I}^{2}{{trace}\left( {y_{k}y_{k}^{H}D_{k}^{I}} \right)}}}{{R_{k}\left( \rho_{I} \right)}}} + {\log\left( {{R_{k}\left( \rho_{I} \right)}} \right)}}};$$M_{\rho_{I}} = {\frac{{\underset{k = 1}{\sum\limits^{K}}{{trace}\left( {y_{k}{y_{k}^{H}\left( {D_{k}^{S} + {\sigma^{2}I}} \right)}} \right)}} + {\rho_{I}^{2}{{trace}\left( {y_{k}y_{k}^{H}D_{k}^{I}} \right)}}}{\sum\limits_{k = 1}^{K}\frac{{R_{k}\left( \rho_{I} \right)}}{K}} + {K\;{\log\left( \frac{\sum\limits_{k = 1}^{K}{{R_{k}\left( \rho_{I} \right)}}}{K} \right)}}}$${M_{\rho_{I,{cmi}}} = {{\sum\limits_{k = 1}^{K}\frac{{{trace}\left( {y_{k}{y_{k}^{H}\left( {D_{k}^{S} + {\sigma^{2}I}} \right)}} \right)} + {\rho_{I}^{2}{{trace}\left( {y_{k}y_{k}^{H}{D_{k}^{I}({cmi})}} \right)}}}{{R_{k}\left( {\rho_{I},{cmi}} \right)}}} + {\log\left( {{R_{k}\left( {\rho_{I},{cmi}} \right)}} \right)}}};{or}$${M_{\rho_{I},{cmi}} \approx {\frac{{\underset{k = 1}{\sum\limits^{K}}{{trace}\left( {y_{k}{y_{k}^{H}\left( {D_{k}^{S} + {\sigma^{2}I}} \right)}} \right)}} + {\rho_{I}^{2}{{trace}\left( {y_{k}y_{k}^{H}{D_{k}^{I}({cmi})}} \right)}}}{\sum\limits_{k = 1}^{K}\frac{{R_{k}\left( {\rho_{I},{cmi}} \right)}}{K}} + {K\;{\log\left( \frac{\sum\limits_{k = 1}^{K}{{R_{k}\left( {\rho_{I},{cmi}} \right)}}}{K} \right)}}}},$where M_(ρ) _(I) represents the metric in one CRS antenna port case andM_(ρ) _(I) _(,cmi) represent the metric in two CRS antenna port case,y_(k)=H_(k) ^(S)x_(k) ^(S)+ρ_(I)H_(k) ^(I)x_(k) ^(I)+n_(k), H_(k) ^(m)represents an effective channel matrix from a serving evolved node B(eNB) to a user equipment (UE) for m=S and from an interfering cell tothe UE for m=I, where ρ_(I) represents a TPR of an interfering signal,x_(k) ^(m)=[x_(k) ^(m,1), . . . , x_(k) ^(m,l) ^(m) ]^(T) is a l_(m)×1transmit signal vector, l_(m) indicates a number of transmission layers,n_(k) is an additive white Gaussian noise (AWGN) vector with covarianceE{n_(k)n_(k) ^(H)}=σ²I, K is a integer, |R_(k)(ρ_(I))| denotes adeterminant of matrix R_(k)(ρ_(I))=R_(k) ^(S)+ρ_(I) ²R_(k) ^(I)+σ²I,$R_{k}^{S} = \begin{bmatrix}r_{k,00}^{S} & r_{k,01}^{S} \\r_{k,10}^{S} & r_{k,11}^{S}\end{bmatrix}$ $R_{k}^{I} = \begin{bmatrix}r_{k,00}^{I} & r_{k,01}^{I} \\r_{k,10}^{I} & r_{k,11}^{I}\end{bmatrix}$ ${D_{k}^{S} = \begin{bmatrix}r_{k,11}^{S} & {- r_{k,01}^{S}} \\{- r_{k,10}^{S}} & r_{k,00}^{S}\end{bmatrix}},{and}$ ${D_{k}^{I} = \begin{bmatrix}r_{k,11}^{I} & {- r_{k,01}^{I}} \\{- r_{k,10}^{I}} & r_{k,00}^{I}\end{bmatrix}},$ and |R_(k)(ρ_(I), cmi)| denotes a determinant of matrixR_(k)(ρ_(I), cmi)=R_(k) ^(S)+ρ_(I) ²R_(k) ^(I)(cmi)+σ²I, where$\begin{matrix}{{R_{k}^{I}({cmi})} = {G_{k}^{I}{P^{I,l_{I},p}\left( P^{I,l_{I},p} \right)}^{H}\left( G_{k}^{I} \right)^{H}}} \\{{= \begin{bmatrix}{r_{k,00}^{I}({cmi})} & {r_{k,01}^{I}({cmi})} \\{r_{k,10}^{I}({cmi})} & {r_{k,11}^{I}({cmi})}\end{bmatrix}},{and}} \\{{{D_{k}^{I}({cmi})} = \begin{bmatrix}{r_{k,11}^{I}({cmi})} & {- {r_{k,01}^{I}({cmi})}} \\{- {r_{k,10}^{I}({cmi})}} & {r_{k,00}^{I}({cmi})}\end{bmatrix}},}\end{matrix}$ then R_(k) ⁻¹(ρ_(I), cmi) is as follows:${{R_{k}^{- 1}\left( {\rho_{I},{cmi}} \right)} = \frac{D_{k}^{S} + {\rho_{I}^{2}{D_{k}^{I}({cmi})}} + {\sigma^{2}I}}{{R_{k}\left( {\rho_{I},{cmi}} \right)}}},$wherein cmi∈{0,1,2,3,4} with cmi=i (for i∈{0,1,2,3}) corresponding torank 1 with a precoding index of p=i, and cmi=4 corresponding to rank 2and SFBC, and wherein there are 5 possible hypotheses for cmi and 3possible hypotheses for ρ_(I).
 10. The method of claim 8, wherein theprecoding matrix index for the received signal of rank 2 or aserving-signal-cancelled received signal of rank 2 is identified basedon${M_{I} = {{\frac{1}{K}{\sum\limits_{k = 1}^{K}\;{f\left( \beta_{k,I} \right)}}} \approx {E\left\{ {f\left( \beta_{k,I} \right)} \right\}\mspace{14mu}{and}}}}\;$${M_{Q} = {{\frac{1}{K}{\sum\limits_{k = 1}^{K}\;{f\left( \beta_{k,Q} \right)}}} \approx {E\left\{ {f\left( \beta_{k,Q} \right)} \right\}}}},$wherein a non-linear operation f(.) has a property thatE{f(β_(k,I))}≠E{f(β_(k,Q))}, wherein the non-linear operation f(.)includes f(β_(k,I))=|β_(k,I)| and f(β_(k,I))=|β_(k,I)|², where aprecoding identification rule is $\hat{p} = \left\{ {\begin{matrix}0 & {M_{Q} > M_{I}} \\1 & {M_{Q} < M_{I}}\end{matrix}.} \right.$
 11. An apparatus, comprising: an antenna forreceiving a signal including a serving signal and an interferencesignal; and a processor configured to: apply a Gaussian approximation(GA) on the serving signal and the interference signal; determine, forone or more hypotheses, likelihood metrics for a rank of theinterference signal, a precoding matrix index, and power on theGA-applied interference signal, wherein each hypothesis is a uniquecombination of a traffic to pilot ratio (TPR) from one or more TPRs ofthe interference signal and a covariance matrix index (CMI) from one ormore CMIs; and determine a TPR from at least one of the hypotheses thatmaximize the likelihood metrics.
 12. The apparatus of claim 11, whereinthe processor is further configured to: determine, jointly, a maximumlikelihood (ML) solution of rank, the TPR, and a precoding matrix indexon the GA-applied serving signal and the GA-applied interference signal;and determine sequentially, the rank of the interference signal based onthe jointly determined ML solution.
 13. The apparatus of claim 12,wherein the processor is further configured to determine a covariancematrix on the received signal after the serving signal is cancelled fromthe received signal.
 14. The apparatus of claim 12, wherein theprocessor is further configured to: determine if the rank is 1; if therank is not 1 then determine if transmit diversity is present; if thetransmit diversity is not present then determine that the rank is 2;determine the precoding matrix index if the rank is 1, the transmitdiversity is present, or if the rank is 2; and return the determinationsof the TPR, the rank, and the precoding matrix index.
 15. The apparatusof claim 13, wherein the processor is further configured to: determineif the rank is 1; if the rank is not 1 then determine if transmitdiversity is present; if the transmit diversity is not present thendetermine that the rank is 2; determine the precoding matrix index ifthe rank is 1, the transmit diversity is present, or if the rank is 2;and return the determinations of the TPR, the rank, and the precodingmatrix index.
 16. The apparatus of claim 14, wherein the processor isfurther configured to determine the ML solution of rank, TPR, andprecoding matrix index for at least one cell-specific reference signal(CRS) antenna port.
 17. The apparatus of claim 15, wherein the processoris further configured to determine the ML solution of rank, TPR, andprecoding matrix index for at least one cell-specific reference signal(CRS) antenna port.
 18. The apparatus of claim 16, wherein the processoris further configured to determine a likelihood metric selected from oneof:${M_{\rho_{I}} = {{\sum\limits_{k = 1}^{K}\;\frac{{{trace}\left( {y_{k}{y_{k}^{H}\left( {D_{k}^{S} + {\sigma^{2}I}} \right)}} \right)} + {\rho_{I}^{2}{{trace}\left( {y_{k}y_{k}^{H}D_{k}^{I}} \right)}}}{{R_{k}\left( \rho_{I} \right)}}} + {\log\left( {{R_{k}\left( \rho_{I} \right)}} \right)}}};$$M_{\rho_{I}} = {\frac{{\sum\limits_{k = 1}^{K}{{trace}\left( {y_{k}{y_{k}^{H}\left( {D_{k}^{S} + {\sigma^{2}I}} \right)}} \right)}} + {\rho_{I}^{2}{{trace}\left( {y_{k}y_{k}^{H}D_{k}^{I}} \right)}}}{\sum\limits_{k = 1}^{K}\frac{{R_{k}\left( \rho_{I} \right)}}{K}} + {K\;{\log\left( \frac{\sum\limits_{k = 1}^{K}{{R_{k}\left( \rho_{I} \right)}}}{K} \right)}}}$${M_{\rho_{I,{cmi}}} = {{\sum\limits_{k = 1}^{K}\;\frac{{{trace}\left( {y_{k}{y_{k}^{H}\left( {D_{k}^{S} + {\sigma^{2}I}} \right)}} \right)} + {\rho_{I}^{2}{{trace}\left( {y_{k}y_{k}^{H}{D_{k}^{I}({cmi})}} \right)}}}{{R_{k}\left( {\rho_{I},{cmi}} \right)}}} + {\log\left( {{R_{k}\left( {\rho_{I},{cmi}} \right)}} \right)}}};{or}$${M_{\rho_{I},{cmi}} \approx {\frac{{\sum\limits_{k = 1}^{K}{{trace}\left( {y_{k}{y_{k}^{H}\left( {D_{k}^{S} + {\sigma^{2}I}} \right)}} \right)}} + {\rho_{I}^{2}{{trace}\left( {y_{k}y_{k}^{H}{D_{k}^{I}({cmi})}} \right)}}}{\sum\limits_{k = 1}^{K}\frac{{R_{k}\left( {\rho_{I},{cmi}} \right)}}{K}} + {K\;{\log\left( \frac{\sum\limits_{k = 1}^{K}{{R_{k}\left( {\rho_{I},{cmi}} \right)}}}{K} \right)}}}},$where M_(ρ) _(I) represents the metric in one CRS antenna port case andM_(ρ) _(I) _(,cmi) represent the metric in two CRS antenna port case,y_(k)=H_(k) ^(S)x_(k) ^(S)+ρ_(I)H_(k) ^(I)x_(k) ^(I)+n_(k), H_(k) ^(m)represents an effective channel matrix from a serving evolved node B(eNB) to a user equipment (UE) for m=S and from an interfering cell tothe UE for m=I, where ρ_(I) represents a TPR of an interfering signal,x_(k) ^(m)=[x_(k) ^(m,1), . . . , x_(k) ^(m,l) ^(m) ]^(T) is a l_(m)×1transmit signal vector, l_(m) indicates a number of transmission layers,n_(k) is an additive white Gaussian noise (AWGN) vector with covarianceE{n_(k)n_(k) ^(H)}=σ²I, K is a integer, |R_(k)(ρ_(I))| denotes adeterminant of matrix R_(k)(ρ_(I))=R_(k) ^(S)+ρ_(I) ²R_(k) ^(I)+σ²I,$R_{k}^{S} = \begin{bmatrix}r_{k,00}^{S} & r_{k,01}^{S} \\r_{k,10}^{S} & r_{k,11}^{S}\end{bmatrix}$ $R_{k}^{I} = \begin{bmatrix}r_{k,00}^{I} & r_{k,01}^{I} \\r_{k,10}^{I} & r_{k,11}^{I}\end{bmatrix}$ ${D_{k}^{S} = \begin{bmatrix}r_{k,11}^{S} & {- r_{k,01}^{S}} \\{- r_{k,10}^{S}} & r_{k,00}^{S}\end{bmatrix}},{and}$ ${D_{k}^{I} = \begin{bmatrix}r_{k,11}^{I} & {- r_{k,01}^{I}} \\{- r_{k,10}^{I}} & r_{k,00}^{I}\end{bmatrix}},$ and |R_(k)(ρ_(I),cmi)| denotes a determinant of matrixR_(k)(ρ_(I),cmi)=R_(k) ^(S)+ρ_(I) ^(S)R_(k) ^(I)(cmi)+σ²I, where$\begin{matrix}{{R_{k}^{I}({cmi})} = {G_{k}^{I}{P^{I,l_{I},p}\left( P^{I,l_{I},p} \right)}^{H}\left( G_{k}^{I} \right)^{H}}} \\{{= \begin{bmatrix}{r_{k,00}^{I}({cmi})} & {r_{k,01}^{I}({cmi})} \\{r_{k,10}^{I}({cmi})} & {r_{k,11}^{I}({cmi})}\end{bmatrix}},{and}} \\{{{D_{k}^{I}({cmi})} = \begin{bmatrix}{r_{k,11}^{I}({cmi})} & {- {r_{k,01}^{I}({cmi})}} \\{- {r_{k,10}^{I}({cmi})}} & {r_{k,00}^{I}({cmi})}\end{bmatrix}},}\end{matrix}$ then R_(k) ⁻¹(ρ_(I), cmi) is as follows:${{R_{k}^{- 1}\left( {\rho_{I},{cmi}} \right)} = \frac{D_{k}^{S} + {\rho_{I}^{2}{D_{k}^{I}({cmi})}} + {\sigma^{2}I}}{{R_{k}\left( {\rho_{I},{cmi}} \right)}}},$wherein cmi {0,1,2,3,4}, and wherein there are five possible hypothesesfor cmi and three possible hypotheses for ρ_(I).
 19. The apparatus ofclaim 17, wherein the processor is further configured to determine alikelihood metric selected from one of:${M_{\rho_{I}} = {{\sum\limits_{k = 1}^{K}\;\frac{{{trace}\left( {y_{k}{y_{k}^{H}\left( {D_{k}^{S} + {\sigma^{2}I}} \right)}} \right)} + {\rho_{I}^{2}{{trace}\left( {y_{k}y_{k}^{H}D_{k}^{I}} \right)}}}{{R_{k}\left( \rho_{I} \right)}}} + {\log\left( {{R_{k}\left( \rho_{I} \right)}} \right)}}};$$M_{\rho_{I}} = {\frac{{\sum\limits_{k = 1}^{K}{{trace}\left( {y_{k}{y_{k}^{H}\left( {D_{k}^{S} + {\sigma^{2}I}} \right)}} \right)}} + {\rho_{I}^{2}{{trace}\left( {y_{k}y_{k}^{H}D_{k}^{I}} \right)}}}{\sum\limits_{k = 1}^{K}\frac{{R_{k}\left( \rho_{I} \right)}}{K}} + {K\;{\log\left( \frac{\sum\limits_{k = 1}^{K}{{R_{k}\left( \rho_{I} \right)}}}{K} \right)}}}$${M_{\rho_{I,{cmi}}} = {{\sum\limits_{k = 1}^{K}\;\frac{{{trace}\left( {y_{k}{y_{k}^{H}\left( {D_{k}^{S} + {\sigma^{2}I}} \right)}} \right)} + {\rho_{I}^{2}{{trace}\left( {y_{k}y_{k}^{H}{D_{k}^{I}({cmi})}} \right)}}}{{R_{k}\left( {\rho_{I},{cmi}} \right)}}} + {\log\left( {{R_{k}\left( {\rho_{I},{cmi}} \right)}} \right)}}};{or}$${M_{\rho_{I},{cmi}} \approx {\frac{{\sum\limits_{k = 1}^{K}{{trace}\left( {y_{k}{y_{k}^{H}\left( {D_{k}^{S} + {\sigma^{2}I}} \right)}} \right)}} + {\rho_{I}^{2}{{trace}\left( {y_{k}y_{k}^{H}{D_{k}^{I}({cmi})}} \right)}}}{\sum\limits_{k = 1}^{K}\frac{{R_{k}\left( {\rho_{I},{cmi}} \right)}}{K}} + {K\;{\log\left( \frac{\sum\limits_{k = 1}^{K}{{R_{k}\left( {\rho_{I},{cmi}} \right)}}}{K} \right)}}}},$where M_(ρ) _(I) represents the metric in one CRS antenna port case andM_(ρ) _(I) _(,cmi) represent the metric in two CRS antenna port case,y_(k)=H_(k) ^(S)x_(k) ^(S)+ρ_(I)H_(k) ^(I)x_(k) ^(I)+n_(k), H_(k) ^(m)represents an effective channel matrix from a serving evolved node B(eNB) to a user equipment (UE) for m=S and from an interfering cell tothe UE for m=I, where ρ_(I) represents a TPR of an interfering signal,x_(k) ^(m)=[x_(k) ^(m,1), . . . , x_(k) ^(m,l) ^(m) ]^(T) is a l_(m)×1transmit signal vector, l_(m) indicates a number of transmission layers,n_(k) is an additive white Gaussian noise (AWGN) vector with covarianceE{n_(k)n_(k) ^(H)}=σ²I, K is a integer, |R_(k)(ρ_(I))| denotes adeterminant of matrix R_(k)(ρ_(I))=R_(k) ^(S)+ρ_(I) ²R_(k) ^(I)+σ²I,$R_{k}^{S} = \begin{bmatrix}r_{k,00}^{S} & r_{k,01}^{S} \\r_{k,10}^{S} & r_{k,11}^{S}\end{bmatrix}$ $R_{k}^{I} = \begin{bmatrix}r_{k,00}^{I} & r_{k,01}^{I} \\r_{k,10}^{I} & r_{k,11}^{I}\end{bmatrix}$ ${D_{k}^{S} = \begin{bmatrix}r_{k,11}^{S} & {- r_{k,01}^{S}} \\{- r_{k,10}^{S}} & r_{k,00}^{S}\end{bmatrix}},{and}$ ${D_{k}^{I} = \begin{bmatrix}r_{k,11}^{I} & {- r_{k,01}^{I}} \\{- r_{k,10}^{I}} & r_{k,00}^{I}\end{bmatrix}},$ and |R_(k)(ρ_(I),cmi)| denotes a determinant of matrixR_(k)(ρ_(I),cmi)=R_(k) ^(S)+ρ_(I) ²R_(k) ^(I)(cmi)+σ²I, where$\begin{matrix}{{R_{k}^{I}({cmi})} = {G_{k}^{I}{P^{I,l_{I},p}\left( P^{I,l_{I},p} \right)}^{H}\left( G_{k}^{I} \right)^{H}}} \\{{= \begin{bmatrix}{r_{k,00}^{I}({cmi})} & {r_{k,01}^{I}({cmi})} \\{r_{k,10}^{I}({cmi})} & {r_{k,11}^{I}({cmi})}\end{bmatrix}},{and}} \\{{{D_{k}^{I}({cmi})} = \begin{bmatrix}{r_{k,11}^{I}({cmi})} & {- {r_{k,01}^{I}({cmi})}} \\{- {r_{k,10}^{I}({cmi})}} & {r_{k,00}^{I}({cmi})}\end{bmatrix}},}\end{matrix}$ then R_(k) ⁻¹(ρ_(I),cmi) is as follows:${{R_{k}^{- 1}\left( {\rho_{I},{cmi}} \right)} = \frac{D_{k}^{S} + {\rho_{I}^{2}{D_{k}^{I}({cmi})}} + {\sigma^{2}I}}{{R_{k}\left( {\rho_{I},{cmi}} \right)}}},$wherein cmi ∈{0,1,2,3,4}, and wherein there are five possible hypothesesfor cmi and three possible hypotheses for ρ_(I).
 20. The apparatus ofclaim 18, wherein the processor is further configured to identify aprecoding matrix index for the received signal of rank 2 or aserving-signal-cancelled received signal of rank 2 based on${M_{I} = {{\frac{1}{K}{\sum\limits_{k = 1}^{K}\;{f\left( \beta_{k,I} \right)}}} \approx {E\left\{ {f\left( \beta_{k,I} \right)} \right\}\mspace{14mu}{and}}}}\;$${M_{Q} = {{\frac{1}{K}{\sum\limits_{k = 1}^{K}\;{f\left( \beta_{k,Q} \right)}}} \approx {E\left\{ {f\left( \beta_{k,Q} \right)} \right\}}}},$wherein a non-linear operation f(.) has a property thatE{f(β_(k,I))}≠E{f(β_(k,Q))}, wherein the non-linear operation f(.)includes f(β_(k,I))=|β_(k,I)| and f(β_(k,I))=|β_(k,I)|², where aprecoding identification rule is $\hat{p} = \left\{ {\begin{matrix}0 & {M_{Q} > M_{I}} \\1 & {M_{Q} < M_{I}}\end{matrix}.} \right.$